# Unified Fock space representation of fractional quantum Hall states

## TL;DR

This paper introduces a unified Fock space representation for fractional quantum Hall states, using a two-body squeezing operator that applies to both bosonic and fermionic states, revealing fundamental recurrence relations.

## Contribution

It provides an explicit Fock space representation of fractional quantum Hall wavefunctions via a two-body squeezing operator applicable to both bosons and fermions.

## Key findings

- Unified operator representation for bosonic and fermionic states
- Revealed recurrence relations linked to particle statistics
- Expressed wavefunctions as Jastrow operators on simple patterns

## Abstract

Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read and Read-Rezayi wavefunctions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows to point out two different recurrence relations for the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states. Here we provide an explicit Fock space representation for these wavefunctions by introducing a two-body squeezing operator which represents them as a Jastrow operator applied to reference states, which are in general simple periodic one dimensional patterns. Remarkably, this operator representation is the same for bosons and fermions, and the different nature of the two recurrence relations is an outcome of particle statistics.